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Journal of Zhejiang University SCIENCE A 2004 Vol.5 No.11 P.1466-1470


Generalized solutions to the Benjamin-Ono equations in sense of Colombeau

Author(s):  JIN Xiao-gang, YANG Jian-gang, LIN Jie

Affiliation(s):  Institute of Artificial Intelligence, College of Computer Science, Zhejiang University, Hangzhou 310027, China

Corresponding email(s):   xiaogangj@cise.zju.edu.cn

Key Words:  B-O equation, Algebra of generalized solution, Hilbert transform

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JIN Xiao-gang, YANG Jian-gang, LIN Jie. Generalized solutions to the Benjamin-Ono equations in sense of Colombeau[J]. Journal of Zhejiang University Science A, 2004, 5(11): 1466-1470.

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This paper discusses the existence and uniqueness of the generalized solution in the sense of Colombeau to the Benjamin-Ono (B-O) equation and the relationship between the new generalized solution and the classical solution.

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[7] Colombeau, J.F., 1990. Multiplication of Distributions. Bulletin in A.M.S., 23:251-268.

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[9] Iorio, R.J., 1986. On the cauchy problem for the Benjamin-Ono equation. Comm. P. D. E., 11:1031-1081.

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[11] Nakamura, A., 1979. Bäcklund transform and conservation laws of the Benjamin-Ono equation. J. PhYS. Soc., 47:1335-1340.

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